scholarly journals Ship waves on uniform shear current at finite depth: wave resistance and critical velocity

2016 ◽  
Vol 791 ◽  
pp. 539-567 ◽  
Author(s):  
Yan Li ◽  
Simen Å Ellingsen
Keyword(s):  
Froude Number ◽  
Critical Velocity ◽  
Water Depth ◽  
Deep Water ◽  
Wave Resistance ◽  
Ship Motion ◽  
Ship Waves ◽  
Lateral Wave ◽  
Shear Current ◽  
Finite Water Depth

We present a comprehensive theory for linear gravity-driven ship waves in the presence of a shear current with uniform vorticity, including the effects of finite water depth. The wave resistance in the presence of shear current is calculated for the first time, containing in general a non-zero lateral component. While formally apparently a straightforward extension of existing deep water theory, the introduction of finite water depth is physically non-trivial, since the surface waves are now affected by a subtle interplay of the effects of the current and the sea bed. This becomes particularly pronounced when considering the phenomenon of critical velocity, the velocity at which transversely propagating waves become unable to keep up with the moving source. The phenomenon is well known for shallow water, and was recently shown to exist also in deep water in the presence of a shear current (Ellingsen, J. Fluid Mech., vol. 742, 2014, R2). We derive the exact criterion for criticality as a function of an intrinsic shear Froude number $S\sqrt{b/g}$ ($S$ is uniform vorticity, $b$ size of source), the water depth and the angle between the shear current and the ship’s motion. Formulae for both the normal and lateral wave resistance forces are derived, and we analyse their dependence on the source velocity (or Froude number $Fr$) for different amounts of shear and different directions of motion. The effect of the shear current is to increase wave resistance for upstream ship motion and decrease it for downstream motion. Also the value of $Fr$ at which $R$ is maximal is lowered for upstream and increased for downstream directions of ship motion. For oblique angles between ship motion and current there is a lateral wave resistance component which can amount to 10–20 % of the normal wave resistance for side-on shear and $S\sqrt{b/g}$ of order unity. The theory is fully laid out and far-field contributions are carefully separated off by means of Cauchy’s integral theorem, exposing potential pitfalls associated with a slightly different method (Sokhotsky–Plemelj) used in several previous works.

Waves and Wave Resistance for Air-Cushion Vehicles with Time-Dependent Cushion Pressures

1978 ◽  
Vol 22 (03) ◽  
pp. 170-177
Author(s):  
H. J. Haussling ◽  
R. T. Van Eseltine
Keyword(s):  
Shallow Water ◽  
Froude Number ◽  
Water Depth ◽  
Critical Frequency ◽  
Wave Resistance ◽  
Time Dependent ◽  
Length Ratio ◽  
Wave Patterns ◽  
Air Cushion ◽  
Air Cushion Vehicles

Wave patterns and wave resistance are computed for air-cushion vehicles with time-dependent cushion pressures moving at uniform speed over deep and shallow water. The effect of beam-to-length ratio, Froude number, and water depth on the resistance is investigated. The resistance is found to exhibit a distinctive behavior at a critical frequency. This behavior corresponds to a singularity in the resistance at the critical frequency. The importance of this behavior is found to diminish with decreasing beam-to-length ratio and increasing Froude number.

Interference Resistance of Multi-Hull Vessels in Finite-Depth Waters

2012 ◽  
Author(s):  
Alexia Aubault ◽  
Ronald W. Yeung
Keyword(s):  
Froude Number ◽  
Water Depth ◽  
High Speed ◽  
Fuel Efficiency ◽  
Finite Depth ◽  
Wave Resistance ◽  
Optimized Design ◽  
Near Shore ◽  
Geometric Variables ◽  
Depth Water

As high-speed ferry traffic is growing in near-shore areas, fuel efficiency of vessel operating in finite-depth waters becomes more critical. This can be achieved by introducing multi-hulls and minimizing the wave resistance by a proper configuration of the hulls. The wave resistance of thin-hulled vessels can be computed within Michell’s theory. Based on this principle, Yeung et al. (2004) introduced a formulation of the interference wave resistance on multi-hull vessels in deep water, after linearization of the boundary conditions. The method is generalized to any water-depth in this paper. Havelock (1921) derived the wave resistance of a single-hull vessel in finite-depth water. An expression of the interaction resistance between two hulls in finite-depth waters is derived, using a distribution of Havelock sources on the hulls. It is shown that the interference resistance may be defined as a function of geometric variables and a length-based Froude number and depth-based Froude number. The effect of sub-criticality, criticality and supercriticality of depth-based Froude number on the interference resistance is explored. The computation of the total wave resistance of two hulls is extended to vessels with any number of hulls. The application of this solution method is demonstrated. With the use of the formulation, multi-hull designs are optimized with respect to the geometric distribution of hulls as well as forward speed and water depth. The design of multi-hull vessels illustrates how an optimized design is quickly obtained. Design decisions early in the design process can therefore be facilitated by this procedure.

scholarly journals SHIP WAVES IN SHALLOW WATER AND THEIR EFFECTS ON MOORED SMALL VESSEL

1984 ◽  
Vol 1 (19) ◽  
pp. 218 ◽  
Author(s):  
Katsuhiko Kurata ◽  
Kazuki Oda
Keyword(s):  
Shallow Water ◽  
Froude Number ◽  
Water Depth ◽  
Small Vessel ◽  
Ship Waves ◽  
Wide Range

The characteristics of ship-generated waves in shallow water and the motions of moored small vessel induced by the ship waves were investigated in a wide range of water-depth and ship-length Froude Numbers. The maximum heights and periods of ship waves were obtained as functions of Froude Number. The relationships between maximum angular and translatory displacements of moored vessel and the maximum ship waves were determined.

scholarly journals HIGH ORDER NONLINEAR WAVE INTERACTIONS FROM DEEP TO FINITE WATER DEPTH WITH BOTTOM TOPOGRAPHY CHANGE

2020 ◽  
pp. 24
Author(s):  
Zuorui Lyu ◽  
Hiroaki Kashima ◽  
Nobuhito Mori
Keyword(s):  
Nonlinear Wave ◽  
Water Depth ◽  
Deep Water ◽  
Modulational Instability ◽  
High Order ◽  
Long Distance ◽  
Freak Wave ◽  
Wave Evolution ◽  
Finite Water Depth ◽  
Skewness And Kurtosis

In recent years, freak wave/rouge wave has become an important problem in science and engineering. Modulational instability is considered to be an important factor leading to freak wave in the wave evolution of deep water, and Janssen (2003) defined Benjamin-Feir index (BFI) to reflect it. Mori and Janssen (2006) gave the occurrence probability of freak waves based on a weakly non-Gaussian theory, and distribution of wave height is determined by skewness and kurtosis of surface elevation to a considerable extent in deep water. According to observational record, freak wave has not only been found in deep water in the ocean, but also been observed in shallow water and coastal areas. In the process of water wave entering continental shelf, water depth is changing with mild slope after a long distance propagation. This study focus on investigating how water depth affect skewness and kurtosis in the high order nonlinear wave evolution from deep water to finite water depth in two-dimension.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/a8LiJvXWRrw

Finite-amplitude steady-state wave groups with multiple near-resonances in finite water depth

2019 ◽  
Vol 867 ◽  
pp. 348-373 ◽  
Author(s):  
Z. Liu ◽  
D. Xie
Keyword(s):  
Steady State ◽  
Water Depth ◽  
Deep Water ◽  
High Frequency ◽  
Finite Amplitude ◽  
Wave Groups ◽  
State Wave ◽  
Resonant Interactions ◽  
Frequency Components ◽  
Finite Water Depth

Finite-amplitude wave groups with multiple near-resonances are investigated to extend the existing results due to Liu et al. (J. Fluid Mech., vol. 835, 2018, pp. 624–653) from steady-state wave groups in deep water to steady-state wave groups in finite water depth. The slow convergence rate of the series solution in the homotopy analysis method and extra unpredictable high-frequency components in finite water depth make it hard to obtain finite-amplitude wave groups accurately. To overcome these difficulties, a solution procedure that combines the homotopy analysis method-based analytical approach and Galerkin method-based numerical approaches has been used. For weakly nonlinear wave groups, the continuum of steady-state resonance from deep water to finite water depth is established. As nonlinearity increases, the frequency bands broaden and more steady-state wave groups are obtained. Finite-amplitude wave groups with steepness no less than $0.20$ are obtained and the resonant sets configuration of steady-state wave groups are analysed in different water depths. For waves in deep water, the majority of non-trivial components appear around the primary ones due to four-wave, six-wave, eight-wave or even ten-wave resonant interactions. The dominant role of four-wave resonant interactions for steady-state wave groups in deep water is demonstrated. For waves in finite water depth, additional non-trivial high-frequency components appear in the spectra due to three-wave, four-wave, five-wave or even six-wave resonant interactions with the components around the primary ones. The amplitude of these high-frequency components increases further as the water depth decreases. Resonances composed by components only around the primary ones are suppressed while resonances composed by components around the primary ones and from the high-frequency domain are enhanced. The spectrum of steady-state resonant wave groups changes with the water depth and the significant role of three-wave resonant interactions in finite water depth is demonstrated.

Ship Springing Response in Finite Water Depth

2012 ◽  
Vol 56 (02) ◽  
pp. 80-90
Author(s):  
Jelena Vidic-Perunovic
Keyword(s):  
Relative Motion ◽  
Water Depth ◽  
Deep Water ◽  
Bending Moment ◽  
Intermediate Water ◽  
Short Term ◽  
Strip Theory ◽  
Influence Of Water ◽  
Finite Water Depth ◽  
Wave Induced

The influence of water depth on the vertical wave induced bending moment acting on a hull has been studied. The deep-water second-order nonlinear hydroelastic strip theory, which is based on the relative motion concept, has been generalized to account for a finite water depth. Results for an analytical beam and for a tanker ship are presented and discussed. Short-term load predictions that account for a range of different sea states are given for a tanker ship. As seen from the present study, the effect of intermediate water depth may be a significant factor in calculations of ship springing response.

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